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% DEFINITION DES CARACTERES MATHEMATIQUES B
%------------------------------------------
\def\@setmcodes#1#2#3{{\count0=#1 \count1=#3
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% DEFINITION DES FONTS
%---------------------
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% Note: sometimes called euxm10
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% Note: sometimes called euym10
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\newfam\msxfam \textfont\msxfam=\msx
\newfam\msyfam \textfont\msyfam=\msy

\def\famletter#1{\ifcase #1 0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or
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\edef\fx{\famletter\msxfam}
\edef\fy{\famletter\msyfam}

\def\bbold{\fam\msyfam \msy}

% SYMBOLES B
%-----------
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% used for error messages in Z specs
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% \@myop makes an operator, with a strut to defeat TeX's vertical adjustment.
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\def\_{\leavevmode \vbox{\hrule width0.5em}}

% Save \q as \xq for quantifiers q.
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\def\f#1{\mathrel{\ooalign{\hfil
	$\mapstochar\mkern 3mu\mapstochar\mkern 5mu$\hfil\cr$#1$}}}

\let\mc=\mathchardef

\def	\pow		{\mbox{${\cal P}$}}
\def	\po1		{\mbox{${\cal P}_1$}}
\let	\cross		\times
\def	\lambda		{\@myop{\xlambda}}
\def	\lnot		{\neg\;}
\def	\land		{\mathrel{\wedge}}
\def	\lor		{\mathrel{\vee}}
\let	\implies	\Rightarrow
\let	\iff		\Leftrightarrow
\def	\forall		{\@myop{\xforall}}
\def	\exists		{\@myop{\xexists}}
\def	\semi		{\mathrel{\comp}}
\def	\ssemi		{\mathbin{\rm ;}}
\let	\ensembleVide	\emptyset
\let	\rel		\leftrightarrow
\def	\dom		{\@myop{\sf dom}}
\def	\ran		{\@myop{\sf ran}}
\def	\id		{\@myop{\sf id}}
\def	\comp		{\mathbin{\raise
			0.6ex\hbox{\oalign{\hfil$\scriptscriptstyle
			\rm o$\hfil\cr\hfil$\scriptscriptstyle\rm 9$\hfil}}}}
\def	\para		{\mbox{$\mid\mid$}}
\mc	\dres		"2\fx43
\mc	\rres		"2\fx42
\def	\ndres		{\mathbin{{\dres} \llap{$-$}}}
\def	\nrres		{\mathbin{{\rres}\llap{$-$}}}
\def	\lover		{\mathbin{{\dres} \llap{$-\!\!\!\!-\!$}}}
\def	\rover		{\mathbin{{\rres}\llap{$\!-\!\!\!-$}}}
\let	\fun		\rightarrow
\def	\pfun		{\p\fun}
\def	\pinj		{\p\inj}
\mc	\inj		"3\fx1A
\def	\psurj		{\p\surj}
\mc	\surj		"3\fx10
\def	\bij		{\surj\!\!\!\!\!\!\!\inj}
\def	\nat		{\mbox{${\cal N}$}}
\def	\na1		{\mbox{${\cal N}_1$}}
\def	\num		{\mbox{${\cal Z}$}}
\def	\int		{\mbox{${\cal Z}$}}
\def	\rat		{\mbox{${\cal Q}$}}
\def	\div		{\mathbin{\rm /}}
\def	\mod		{\mathbin{\bf mod}}
\def	\upto		{\mathbin{\ldotp\ldotp}}
\def	\finset		{\mbox{${\cal F}$}}
\def	\finse1		{\mbox{${\cal F}_1$}}
\def	\ffun		{\f\fun}
\def	\finj		{\f\inj}
\def	\seq		{\@myop{\rm seq}}
\def	\cat		{\mathbin{\raise 0.8ex\hbox{$\mathchar"2\fx61$}}}
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%-------------------%
% Debut du document %
%-------------------%

 

\vspace*{4mm}
\bf MACHINE

\hspace*{0.20in}\it TYPES

\vspace*{4mm}
\bf SEES

\hspace*{0.20in}\it BIT\_DEFINITION\rm ,

\hspace*{0.20in}\it BIT\_VECTOR\_DEFINITION\rm ,

\hspace*{0.20in}\it BIT\_VECTOR\_ARITHMETICS\rm ,

\hspace*{0.20in}\it BYTE\_DEFINITION\rm ,

\hspace*{0.20in}\it POWER2

\vspace*{4mm}
\bf CONSTANTS

\hspace*{0.20in}\it UCHAR\_LENGTH\rm ,

\hspace*{0.20in}\it UCHAR\rm ,

\hspace*{0.20in}\it NB\_UCHARS\rm ,

\hspace*{0.20in}\it INST\_SZ\rm ,

\hspace*{0.20in}\it INSTRUCTION\rm ,

\hspace*{0.20in}\it NB\_INSTRUCTIONS\rm ,

\hspace*{0.20in}\it INSTRUCTION\_MAX\rm ,

\hspace*{0.20in}\it instruction\_next\rm ,

\hspace*{0.20in}\it byte\_to\_uchar\rm ,

\hspace*{0.20in}\it uchar\_to\_byte\rm ,

\hspace*{0.20in}\it REGISTER\rm ,

\hspace*{0.20in}\it REGISTER0\rm ,

\hspace*{0.20in}\it REGISTER1

\vspace*{4mm}
\bf PROPERTIES

\hspace*{0.20in}\it UCHAR\_LENGTH  $\in$   $\nat$   $\land$ 

\hspace*{0.20in}\it NB\_UCHARS  $\in$   $\nat$   $\land$ 

\hspace*{0.20in}\it INST\_SZ  $\in$   $\nat$   $\land$ 

\hspace*{0.20in}\it NB\_INSTRUCTIONS  $\in$   $\nat$   $\land$ 

\hspace*{0.20in}\it UCHAR\_LENGTH \rm = \rm 8  $\land$ 

\hspace*{0.20in}\it NB\_UCHARS \rm = \rm 2$^{UCHAR\_LENGTH}$  $\land$ 

\hspace*{0.20in}\it UCHAR \rm = \rm 0 $\upto$ \rm (\it NB\_UCHARS\rm -\rm 1\rm )  $\land$ 

\hspace*{0.20in}\it NB\_INSTRUCTIONS \rm = \rm 2$^{INST\_SZ}$  $\land$ 

\hspace*{0.20in}\it INSTRUCTION\_MAX \rm = \it NB\_INSTRUCTIONS \rm - \rm 1  $\land$ 

\hspace*{0.20in}\it INSTRUCTION \rm = \rm 0 $\upto$ \it INSTRUCTION\_MAX  $\land$ 

\hspace*{0.20in}\it instruction\_next  $\in$  \it INSTRUCTION  $\fun$  \it INSTRUCTION  $\land$ 

\hspace*{0.20in}\it instruction\_next \rm = 

\hspace*{0.40in}\rm \{\it pp\rm , \it qq  $\mid$  \it pp  $\in$  \it INSTRUCTION  $\land$  \it qq  $\in$  \it INSTRUCTION  $\land$  \rm 0  $\leq$  \it pp  $\land$  \it pp $<$ \it NB\_INSTRUCTIONS\rm -\rm 1  $\land$  \it qq \rm = \it pp\rm +\rm 1\rm \}  $\cup$  

\hspace*{0.40in}\rm \{ \it NB\_INSTRUCTIONS\rm -\rm 1  $\mapsto$  \rm 0 \rm \}  $\land$ 

\hspace*{0.20in}\it byte\_to\_uchar  $\in$  \it BYTE  $\fun$  \it UCHAR  $\land$ 

\hspace*{0.20in}\it byte\_to\_uchar \rm =  $\lambda$  \rm (\it vv\rm ) \rm . \rm (\it vv  $\in$  \it BYTE  $\mid$  \it bv\_to\_nat\rm (\it vv\rm )\rm )  $\land$ 

\hspace*{0.20in}\it uchar\_to\_byte  $\in$  \it UCHAR  $\fun$  \it BYTE  $\land$ 

\hspace*{0.20in}\it uchar\_to\_byte \rm = \it byte\_to\_uchar $^{-1}$   $\land$ 

\hspace*{0.20in}\it REGISTER \rm = \rm 0 $\upto$ \rm 2\rm 5\rm 5  $\land$ 

\hspace*{0.20in}\it REGISTER0 \rm = \rm 0 $\upto$ \rm 1\rm 2\rm 7  $\land$ 

\hspace*{0.20in}\it REGISTER1 \rm = \rm 1\rm 2\rm 8 $\upto$ \rm 2\rm 5\rm 5

\vspace*{4mm}
\bf ASSERTIONS

\hspace*{0.20in}\it NB\_UCHARS \rm = \rm 2\rm 5\rm 6\rm ;

\hspace*{0.20in} $\forall$  \rm (\it nn\rm )\rm . \rm (\it nn  $\in$  \it UCHAR  $\implies$  \rm 0  $\leq$  \it nn\rm )\rm ;

\hspace*{0.20in} $\forall$  \rm (\it nn\rm )\rm . \rm (\it nn  $\in$  \it UCHAR  $\implies$  \it nn  $\leq$  \rm 2\rm 5\rm 5\rm )\rm ;

\hspace*{0.20in}\it REGISTER \rm = \it UCHAR\rm ;

\hspace*{0.20in}\bf ran \rm (\it byte\_to\_uchar\rm ) \rm = \it UCHAR

\vspace*{4mm}
\bf END\newpage
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